In this work, we address the multi-label Mumford-Shah problem, i.e., the problem of jointly estimating a partitioning of the domain of the image, and functions defined within regions of the partition. We create algorithms that are efficient, robust to undesirable local minima, and are easy-toimplement. Our algorithms are formulated by slightly modifying the underlying statistical model from which the multilabel Mumford-Shah functional is derived. The advantage of this statistical model is that the underlying variables: the labels and the functions are less coupled than in the original formulation, and the labels can be computed from the functions with more global updates. The resulting algorithms can be tuned to the desired level of locality of the solution: from fully global updates to more local updates. We demonstrate our algorithm on two applications: joint multi-label segmentation and denoising, and joint multi-label motion segmentation and flow estimation. We compare to the stateof-the-art in multi-label Mumford-Shah problems and show that we achieve more promising results.

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We present a new approach to wide baseline matching. We propose to use a hierarchical decomposition of the image domain and coarse-to-fine selection of regions to match. In contrast to interest point matching methods, which sample salient regions to reduce the cost of comparing all regions in two images, our method eliminates regions systematically to achieve efficiency. One advantage of our approach is that it is not restricted to covariant salient regions, which is too restrictive under large viewpoint and leads to few corresponding regions. Affine invariant matching of regions in the hierarchy is achieved efficiently by a coarse-tofine search of the affine space. Experiments on two benchmark datasets shows that our method finds more correct correspondence of the image (with fewer false alarms) than other wide baseline methods on large viewpoint change.

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